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 Volker Patent posted on Monday, September 03, 2012 - 8:11 am
Hi

I have just carried out a regression analysis using bootstrapping. I need to report the regression statistics for each DV and wonder whether there is a significance test for r2 that can be accessed in MPLUS. If not what would be the alternatvie to determining significance of r2. I managed to get the r2 and confidence intervals by using the following line in OUTPUT:

standardized (all) sampstat cinterval (bcbootstrap)

Thanks in advance for your time in replying to this query.

Volker
 Linda K. Muthen posted on Monday, September 03, 2012 - 8:26 am
Mplus gives a standard error and significance test for R-square.
 Volker Patent posted on Tuesday, September 04, 2012 - 6:47 am
Hi Linda, I have not been able to find this in the output. How do I obtain this?

Answering the 'what if not' part of my query I determined the F value using the known pearson R2 as follows:

F=(r2/k)/((1-r2)/(N-k-1)), df=k,N-k-1

but does this hold for a bootstrapped regression?
 Linda K. Muthen posted on Tuesday, September 04, 2012 - 7:29 am
It looks like we don't give a standard error for R-square for bootstrap. The formula you give does not take bootstrapping into account.

If you are interested in the siginficance of R-square, I recommend you use ESTIMATOR=BAYES which allows a non-normally distributed R-square. You can look at the 95% credibility interval.
 Volker Patent posted on Wednesday, September 05, 2012 - 3:08 am
Thank you Linda,

This is helpful. Rerunning the analysis with estimator = Bayes is not possible with bootstrap but I suppose a Bayesian non-normally distibuted R-square is an alternative to using bootstrapping in any case. My reason for using bootstrapping was to fix problems arising from violations of the normality assumption that error terms should be normally distibuted. Is it correct to say that using a Bayesian estimators 'corrects' for the violation that would otherwise occur?

Interestingly the Bayesian estimator produces significant results when the F-test I used initally does not, Also there are differences in the model output and size and significance of the weights, which suggests a different interpretation, so not trivial.

It looks like I need to read up on use of bayesian estimators in regression, for my PhD defence. Could you suggest any references for me to check that discusses use of Bayesian estimation in regression?

Many thanks again.
 Linda K. Muthen posted on Wednesday, September 05, 2012 - 8:54 am
Yes to paragraph one.

Look at TECH8 to see how many iterations were used. Use the FBITERATIONS option to use twice as many iterations as were used in the first analysis.

See Bayesian Analysis under Papers on the website in particular:

Muthén, B. (2010). Bayesian analysis in Mplus: A brief introduction. Technical Report. Version 3.

See also the UCONN 2011 Topic 9 course video and handout on the website.
 Volker Patent posted on Thursday, September 06, 2012 - 4:24 am
Excellent. Many thanks for your advice. :-)
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